1,701 research outputs found
Distributed Maximum Likelihood Sensor Network Localization
We propose a class of convex relaxations to solve the sensor network
localization problem, based on a maximum likelihood (ML) formulation. This
class, as well as the tightness of the relaxations, depends on the noise
probability density function (PDF) of the collected measurements. We derive a
computational efficient edge-based version of this ML convex relaxation class
and we design a distributed algorithm that enables the sensor nodes to solve
these edge-based convex programs locally by communicating only with their close
neighbors. This algorithm relies on the alternating direction method of
multipliers (ADMM), it converges to the centralized solution, it can run
asynchronously, and it is computation error-resilient. Finally, we compare our
proposed distributed scheme with other available methods, both analytically and
numerically, and we argue the added value of ADMM, especially for large-scale
networks
A Parallel Dual Fast Gradient Method for MPC Applications
We propose a parallel adaptive constraint-tightening approach to solve a
linear model predictive control problem for discrete-time systems, based on
inexact numerical optimization algorithms and operator splitting methods. The
underlying algorithm first splits the original problem in as many independent
subproblems as the length of the prediction horizon. Then, our algorithm
computes a solution for these subproblems in parallel by exploiting auxiliary
tightened subproblems in order to certify the control law in terms of
suboptimality and recursive feasibility, along with closed-loop stability of
the controlled system. Compared to prior approaches based on constraint
tightening, our algorithm computes the tightening parameter for each subproblem
to handle the propagation of errors introduced by the parallelization of the
original problem. Our simulations show the computational benefits of the
parallelization with positive impacts on performance and numerical conditioning
when compared with a recent nonparallel adaptive tightening scheme.Comment: This technical report is an extended version of the paper "A Parallel
Dual Fast Gradient Method for MPC Applications" by the same authors submitted
to the 54th IEEE Conference on Decision and Contro
Improving Connectionist Energy Minimization
Symmetric networks designed for energy minimization such as Boltzman machines
and Hopfield nets are frequently investigated for use in optimization,
constraint satisfaction and approximation of NP-hard problems. Nevertheless,
finding a global solution (i.e., a global minimum for the energy function) is
not guaranteed and even a local solution may take an exponential number of
steps. We propose an improvement to the standard local activation function used
for such networks. The improved algorithm guarantees that a global minimum is
found in linear time for tree-like subnetworks. The algorithm, called activate,
is uniform and does not assume that the network is tree-like. It can identify
tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid
local minima along these trees. For acyclic networks, the algorithm is
guaranteed to converge to a global minimum from any initial state of the system
(self-stabilization) and remains correct under various types of schedulers. On
the negative side, we show that in the presence of cycles, no uniform algorithm
exists that guarantees optimality even under a sequential asynchronous
scheduler. An asynchronous scheduler can activate only one unit at a time while
a synchronous scheduler can activate any number of units in a single time step.
In addition, no uniform algorithm exists to optimize even acyclic networks when
the scheduler is synchronous. Finally, we show how the algorithm can be
improved using the cycle-cutset scheme. The general algorithm, called
activate-with-cutset, improves over activate and has some performance
guarantees that are related to the size of the network's cycle-cutset.Comment: See http://www.jair.org/ for any accompanying file
QR Decomposition Framework for Efficient Implementation of Linear Support Vector Machines Using Dual Ascent
Support Vector Machines (SVMs) is a popular method to solve standard machine learning tasks like classification, regression or clustering. There are many algorithms to solve the linear SVM classification problem. However, only a few algorithms are optimized on both per iteration cost and convergence. While fast convergence is essential for solving any optimization problem, per iteration cost is critical in resource-limited environments like dedicated embedded solutions for machine learning problems. In this thesis, we propose a novel approach to solve large-scale linear SVM classification problems. The proposed algorithm has low per iteration cost and also converges faster than existing state-of-art solvers.
There are two significant contributions from this thesis. First, we analyzed and improved the performance of the dual ascent (DA) algorithm, which would serve as the optimizing engine for solving SVM classification problem. An analytical model to evaluate the optimum step size and synchronization period for solving a generic quadratic programming optimization problem using DA is presented. Second, we implement SVM using the improved Dual Ascent algorithm. We also introduce a novel approach to tackle low dimensional classification problems of large data sizes via QR decomposition technique
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